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Adaptive Graph Regularized Deep Semi-nonnegative Matrix Factorization for Data Representation

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Abstract

Recently, matrix factorization-based data representation methods exhibit excellent performance in many real applications. However, traditional deep semi-nonnegative matrix factorization (DSNMF) models the relationship between samples by predefining a fixed graph, which is not optimal and thus cannot exploit the intrinsic local structure among data effectively. In this work, an adaptive graph regularized deep semi-nonnegative matrix factorization (AGRDSNMF) algorithm is proposed for data representation. This proposed AGRDSNMF method can construct an adaptive optimal graph in each layer, whose weights are automatically determined by the probabilities between neighborhood samples. Then the adaptive graph regularizer of each layer is adopted to constrain the corresponding coefficient matrix during decomposition. Therefore, AGRDSNMF can capture the geometric structure of the representation in each layer. Experiments are conducted on COIL20, PIE, and TDT2 datasets, and our AGRDNSMF algorithm can achieve encouraging clustering performance.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China [Grant No. 61603159, 62162033, U21B2027, 61902160], Yunnan Provincial Major Science and Technology Special Plan Projects [Grant No. 202002AD080001, 202103AA080015], Yunnan Foundation Research Projects [Grant No. 202101AT070438, 202101BE070001-056], Excellent Key Teachers of QingLan Project in Jiangsu Province.

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Authors and Affiliations

  1. Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming, 650500, China

    Zhenqiu Shu

  2. School of Computer Engineering, Jiangsu University of Technology, Changzhou, 231001, China

    Yanwu Sun, Jiali Tang & Congzhe You

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  1. Zhenqiu Shu
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  2. Yanwu Sun
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  4. Congzhe You
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Correspondence to Zhenqiu Shu.

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Shu, Z., Sun, Y., Tang, J. et al. Adaptive Graph Regularized Deep Semi-nonnegative Matrix Factorization for Data Representation. Neural Process Lett 54, 5721–5739 (2022). https://doi.org/10.1007/s11063-022-10882-x

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